Flat-Band Enhanced Antiferromagnetic Fluctuations and Superconductivity in Pressurized CsCr$_3$Sb$_5$

The spin dynamics and electronic orders of the kagome system at different filling levels stand as an intriguing subject in condensed matter physics. By first-principles calculations and random phase approximation analyses, we investigate the spin fluctuations and superconducting instabilities in kagome phase of CsCr$_3$Sb$_5$ under high pressure. At the filling level slightly below the kagome flat bands, our calculations reveal strong antiferromagnetic spin fluctuations in CsCr$_3$Sb$_5$, together with a leading $s_{\pm}$-wave and a competing ($d_{xy}$, $d_{x^2-y^2}$)-wave superconducting order. Unlike the general intuition that the flat bands are closely related to the ferromagnetic correlations, here we propose a sublattice-momentum-coupling-driven mechanism for the antiferromagnetic fluctuations enhanced from the unoccupied flat bands. The mechanism is generally applicable to kagome systems where the Fermi level intersects near the flat bands, offering a new perspective for future studies of geometrically frustrated systems.